Question

5. A linear time invariant system has an impulse response, h(t) and input signal, x(t). Use convolution to find the response, y(t) for following signals: x(t)=cos(\pi t)(u(t+1)-u(t-3)) h(t)=u(t) Convolution, y(t) = x(t)*h(t)

          5. A linear time invariant system has an impulse response, h(t) and input signal, x(t).
Use convolution to find the response, y(t) for following signals:
x(t)=cos(\pi t)(u(t+1)-u(t-3))
h(t)=u(t)
Convolution, y(t) = x(t)*h(t)

Added by Josefa L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Stephen Zaffke

Step 1

Since the impulse response h(t) is defined as u(t), which is a unit step function, it is non-zero for t ≥ 0. Therefore, the limits of integration for the convolution integral are t = -∞ to t = ∞. Show more…

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A linear time-invariant system has an impulse response, h(t), and an input signal, x(t). Use convolution to find the response, y(t), for the following signals: x(t) = cos(t)u(t) + 1 - u(t-3) h(t) = u(t) Convolution: y(t) = x(t) * h(t)